Basic Math Examples

- 0.5 (0.3 y^{0.6}) = - 1.5

$- 0.5 (0.3 y^{0.6}) = - 1.5$

Step 1

Multiply

0.3

$0.3$ by

- 0.5

$- 0.5$ .

- 0.15 \cdot y^{0.6} = - 1.5

$- 0.15 \cdot y^{0.6} = - 1.5$

Step 2

Divide each term in

- 0.15 \cdot y^{0.6} = - 1.5

$- 0.15 \cdot y^{0.6} = - 1.5$ by

- 0.15

$- 0.15$ and simplify.

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Step 2.1

Divide each term in

- 0.15 \cdot y^{0.6} = - 1.5

$- 0.15 \cdot y^{0.6} = - 1.5$ by

- 0.15

$- 0.15$ .

\frac{- 0.15 \cdot y^{0.6}}{- 0.15} = \frac{- 1.5}{- 0.15}

$\frac{- 0.15 \cdot y^{0.6}}{- 0.15} = \frac{- 1.5}{- 0.15}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

- 0.15

$- 0.15$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 0.15 \cdot y^{0.6}}{- 0.15} = \frac{- 1.5}{- 0.15}$

Step 2.2.1.2

Divide

$y^{0.6}$ by

$1$ .

$y^{0.6} = \frac{- 1.5}{- 0.15}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide

$- 1.5$ by

$- 0.15$ .

$y^{0.6} = 10$

Step 3

Convert the decimal exponent to a fractional exponent.

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Step 3.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is

$1$ number to the right of the decimal point, place the decimal number over

$10^{1}$

$(10)$ . Next, add the whole number to the left of the decimal.

$y^{0 \frac{6}{10}} = 10$

Step 3.2

Reduce the fraction.

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Step 3.2.1

Convert

$0 \frac{6}{10}$ to an improper fraction.

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Step 3.2.1.1

A mixed number is an addition of its whole and fractional parts.

$y^{0 + \frac{6}{10}} = 10$

Step 3.2.1.2

Add

$0$ and

$\frac{6}{10}$ .

$y^{\frac{6}{10}} = 10$

Step 3.2.2

Cancel the common factor of

$6$ and

$10$ .

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Step 3.2.2.1

Factor

$2$ out of

$6$ .

$y^{\frac{2 (3)}{10}} = 10$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor

$2$ out of

$10$ .

$y^{\frac{2 \cdot 3}{2 \cdot 5}} = 10$

Step 3.2.2.2.2

Cancel the common factor.

$y^{\frac{2 \cdot 3}{2 \cdot 5}} = 10$

Step 3.2.2.2.3

Rewrite the expression.

$y^{\frac{3}{5}} = 10$

Step 4

Raise each side of the equation to the power of

$\frac{1}{0.6}$ to eliminate the fractional exponent on the left side.

${(y^{\frac{3}{5}})}^{\frac{1}{0.6}} = 10^{\frac{1}{0.6}}$

Step 5

Simplify the exponent.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

${(y^{\frac{3}{5}})}^{\frac{1}{0.6}}$ .

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Step 5.1.1.1

Multiply the exponents in

${(y^{\frac{3}{5}})}^{\frac{1}{0.6}}$ .

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Step 5.1.1.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{3}{5} \cdot \frac{1}{0.6}} = 10^{\frac{1}{0.6}}$

Step 5.1.1.1.2

Cancel the common factor of

$0.6$ .

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Step 5.1.1.1.2.1

Factor

$0.6$ out of

$3$ .

$y^{\frac{0.6 (5)}{5} \cdot \frac{1}{0.6}} = 10^{\frac{1}{0.6}}$

Step 5.1.1.1.2.2

Cancel the common factor.

$y^{\frac{0.6 \cdot 5}{5} \cdot \frac{1}{0.6}} = 10^{\frac{1}{0.6}}$

Step 5.1.1.1.2.3

Rewrite the expression.

$y^{\frac{5}{5}} = 10^{\frac{1}{0.6}}$

Step 5.1.1.1.3

Divide

$5$ by

$5$ .

$y^{1} = 10^{\frac{1}{0.6}}$

Step 5.1.1.2

Simplify.

$y = 10^{\frac{1}{0.6}}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

$10^{\frac{1}{0.6}}$ .

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Step 5.2.1.1

Divide

$1$ by

$0.6$ .

$y = 10^{1.\overline{6}}$

Step 5.2.1.2

Raise

$10$ to the power of

$1.\overline{6}$ .

$y = 46.41588833$